Lists model equations, initial parameter values, optimised parameters for fixed effects (population), random effects (deviations from the population mean) and residual error model, as well as the resulting endpoints such as formation fractions and DT50 values. Optionally (default is FALSE), the data are listed in full.
# S3 method for nlme.mmkin summary( object, data = FALSE, verbose = FALSE, distimes = TRUE, alpha = 0.05, ... ) # S3 method for summary.nlme.mmkin print(x, digits = max(3, getOption("digits") - 3), verbose = x$verbose, ...)
| object | an object of class nlme.mmkin |
|---|---|
| data | logical, indicating whether the full data should be included in the summary. |
| verbose | Should the summary be verbose? |
| distimes | logical, indicating whether DT50 and DT90 values should be included. |
| alpha | error level for confidence interval estimation from the t distribution |
| ... | optional arguments passed to methods like |
| x | an object of class summary.nlme.mmkin |
| digits | Number of digits to use for printing |
The summary function returns a list based on the nlme object obtained in the fit, with at least the following additional components
The nlme, mkin and R versions used
The dates where the fit and the summary were produced
The differential equations used in the degradation model
Was maximum or minimum use made of formation fractions
The data
Transformed parameters as used in the optimisation, with confidence intervals
Backtransformed parameters, with confidence intervals if available
The estimated formation fractions derived from the fitted model.
The DT50 and DT90 values for each observed variable.
If applicable, eigenvalues of SFORB components of the model.
Johannes Ranke for the mkin specific parts José Pinheiro and Douglas Bates for the components inherited from nlme
# Generate five datasets following SFO kinetics sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120) dt50_sfo_in_pop <- 50 k_in_pop <- log(2) / dt50_sfo_in_pop set.seed(1234) k_in <- rlnorm(5, log(k_in_pop), 0.5) SFO <- mkinmod(parent = mkinsub("SFO")) pred_sfo <- function(k) { mkinpredict(SFO, c(k_parent = k), c(parent = 100), sampling_times) } ds_sfo_mean <- lapply(k_in, pred_sfo) names(ds_sfo_mean) <- paste("ds", 1:5) ds_sfo_syn <- lapply(ds_sfo_mean, function(ds) { add_err(ds, sdfunc = function(value) sqrt(1^2 + value^2 * 0.07^2), n = 1)[[1]] }) # Evaluate using mmkin and nlme library(nlme) f_mmkin <- mmkin("SFO", ds_sfo_syn, quiet = TRUE, error_model = "tc", cores = 1) f_nlme <- nlme(f_mmkin)#> Warning: Iteration 3, LME step: nlminb() did not converge (code = 1). PORT message: false convergence (8)#> nlme version used for fitting: 3.1.150.1 #> mkin version used for pre-fitting: 0.9.50.4 #> R version used for fitting: 4.0.3 #> Date of fit: Sat Nov 7 13:28:06 2020 #> Date of summary: Sat Nov 7 13:28:06 2020 #> #> Equations: #> d_parent/dt = - k_parent * parent #> #> Data: #> 90 observations of 1 variable(s) grouped in 5 datasets #> #> Model predictions using solution type analytical #> #> Fitted in 0.588 s using 5 iterations #> #> Variance model: Two-component variance function #> #> Mean of starting values for individual parameters: #> parent_0 log_k_parent #> 97.849556 -4.455036 #> #> Fixed degradation parameter values: #> None #> #> Results: #> #> AIC BIC logLik #> 555.792 570.7908 -271.896 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> lower est. upper #> parent_0 94.701336 97.763446 100.82556 #> log_k_parent -5.007574 -4.461767 -3.91596 #> #> Correlation: #> prnt_0 #> log_k_parent 0.024 #> #> Backtransformed parameters with asymmetric confidence intervals: #> lower est. upper #> parent_0 94.701335804 97.76344625 100.82555670 #> k_parent 0.006687109 0.01154195 0.01992142 #> Random effects: #> Formula: list(parent_0 ~ 1, log_k_parent ~ 1) #> Level: ds #> Structure: Diagonal #> parent_0 log_k_parent Residual #> StdDev: 16.65969 3.516961 5.709013 #> #> Variance function: #> Structure: Constant plus proportion of variance covariate #> Formula: ~fitted(.) #> Parameter estimates: #> const prop #> 1.55075176 0.05680853 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 60.05 199.5 #> #> Data: #> ds name time observed predicted residual std standardized #> ds 1 parent 0 103.6 97.42 6.17540 5.748 1.074413 #> ds 1 parent 0 95.9 97.42 -1.52460 5.748 -0.265253 #> ds 1 parent 1 95.4 96.72 -1.31719 5.709 -0.230721 #> ds 1 parent 1 95.3 96.72 -1.41719 5.709 -0.248237 #> ds 1 parent 3 91.6 95.32 -3.71774 5.633 -0.660046 #> ds 1 parent 3 94.5 95.32 -0.81774 5.633 -0.145181 #> ds 1 parent 7 88.1 92.58 -4.47930 5.483 -0.816920 #> ds 1 parent 7 89.6 92.58 -2.97930 5.483 -0.543355 #> ds 1 parent 14 90.3 87.97 2.32502 5.233 0.444318 #> ds 1 parent 14 96.0 87.97 8.02502 5.233 1.533602 #> ds 1 parent 28 80.2 79.44 0.75809 4.772 0.158862 #> ds 1 parent 28 77.9 79.44 -1.54191 4.772 -0.323118 #> ds 1 parent 60 59.3 62.92 -3.61742 3.896 -0.928458 #> ds 1 parent 60 59.6 62.92 -3.31742 3.896 -0.851459 #> ds 1 parent 90 59.4 50.56 8.83825 3.264 2.707613 #> ds 1 parent 90 51.0 50.56 0.43825 3.264 0.134260 #> ds 1 parent 120 38.8 40.63 -1.83247 2.781 -0.658968 #> ds 1 parent 120 38.9 40.63 -1.73247 2.781 -0.623007 #> ds 2 parent 0 103.2 97.17 6.02995 5.734 1.051655 #> ds 2 parent 0 95.1 97.17 -2.07005 5.734 -0.361027 #> ds 2 parent 1 88.3 95.59 -7.28901 5.647 -1.290694 #> ds 2 parent 1 102.4 95.59 6.81099 5.647 1.206048 #> ds 2 parent 3 88.4 92.50 -4.10371 5.479 -0.748984 #> ds 2 parent 3 95.2 92.50 2.69629 5.479 0.492110 #> ds 2 parent 7 83.5 86.63 -3.12863 5.160 -0.606349 #> ds 2 parent 7 96.4 86.63 9.77137 5.160 1.893751 #> ds 2 parent 14 77.3 77.23 0.06920 4.653 0.014871 #> ds 2 parent 14 76.0 77.23 -1.23080 4.653 -0.264497 #> ds 2 parent 28 61.7 61.38 0.31692 3.816 0.083043 #> ds 2 parent 28 56.5 61.38 -4.88308 3.816 -1.279513 #> ds 2 parent 60 35.1 36.31 -1.21343 2.581 -0.470178 #> ds 2 parent 60 32.2 36.31 -4.11343 2.581 -1.593868 #> ds 2 parent 90 21.2 22.20 -0.99906 1.999 -0.499832 #> ds 2 parent 90 23.3 22.20 1.10094 1.999 0.550800 #> ds 2 parent 120 14.1 13.57 0.52931 1.732 0.305638 #> ds 2 parent 120 16.9 13.57 3.32931 1.732 1.922443 #> ds 3 parent 0 92.4 94.12 -1.71979 5.567 -0.308917 #> ds 3 parent 0 94.0 94.12 -0.11979 5.567 -0.021517 #> ds 3 parent 1 95.7 91.97 3.72634 5.450 0.683712 #> ds 3 parent 1 90.8 91.97 -1.17366 5.450 -0.215343 #> ds 3 parent 3 86.7 87.83 -1.12709 5.225 -0.215720 #> ds 3 parent 3 85.8 87.83 -2.02709 5.225 -0.387976 #> ds 3 parent 7 77.1 80.09 -2.98635 4.807 -0.621300 #> ds 3 parent 7 81.5 80.09 1.41365 4.807 0.294104 #> ds 3 parent 14 69.1 68.15 0.95467 4.170 0.228922 #> ds 3 parent 14 62.4 68.15 -5.74533 4.170 -1.377682 #> ds 3 parent 28 49.1 49.34 -0.23911 3.203 -0.074644 #> ds 3 parent 28 47.2 49.34 -2.13911 3.203 -0.667787 #> ds 3 parent 60 21.9 23.58 -1.68477 2.049 -0.822090 #> ds 3 parent 60 23.6 23.58 0.01523 2.049 0.007431 #> ds 3 parent 90 12.4 11.81 0.59388 1.690 0.351500 #> ds 3 parent 90 13.8 11.81 1.99388 1.690 1.180112 #> ds 3 parent 120 4.9 5.91 -1.00993 1.587 -0.636506 #> ds 3 parent 120 7.5 5.91 1.59007 1.587 1.002137 #> ds 4 parent 0 91.8 101.72 -9.92097 5.983 -1.658171 #> ds 4 parent 0 104.6 101.72 2.87903 5.983 0.481194 #> ds 4 parent 1 117.5 101.27 16.23017 5.958 2.723944 #> ds 4 parent 1 99.3 101.27 -1.96983 5.958 -0.330602 #> ds 4 parent 3 94.0 100.37 -6.37355 5.909 -1.078583 #> ds 4 parent 3 98.7 100.37 -1.67355 5.909 -0.283212 #> ds 4 parent 7 109.2 98.60 10.59529 5.812 1.822915 #> ds 4 parent 7 89.2 98.60 -9.40471 5.812 -1.618075 #> ds 4 parent 14 103.3 95.58 7.71609 5.647 1.366386 #> ds 4 parent 14 103.0 95.58 7.41609 5.647 1.313261 #> ds 4 parent 28 90.8 89.82 0.98290 5.333 0.184310 #> ds 4 parent 28 88.7 89.82 -1.11710 5.333 -0.209477 #> ds 4 parent 60 74.8 77.91 -3.10870 4.690 -0.662879 #> ds 4 parent 60 75.3 77.91 -2.60870 4.690 -0.556262 #> ds 4 parent 90 71.1 68.18 2.91738 4.172 0.699234 #> ds 4 parent 90 78.0 68.18 9.81738 4.172 2.353017 #> ds 4 parent 120 59.1 59.67 -0.57073 3.728 -0.153107 #> ds 4 parent 120 53.8 59.67 -5.87073 3.728 -1.574902 #> ds 5 parent 0 94.9 98.38 -3.48183 5.800 -0.600307 #> ds 5 parent 0 101.8 98.38 3.41817 5.800 0.589332 #> ds 5 parent 1 96.1 96.75 -0.65141 5.711 -0.114065 #> ds 5 parent 1 97.1 96.75 0.34859 5.711 0.061040 #> ds 5 parent 3 93.8 93.57 0.22881 5.537 0.041323 #> ds 5 parent 3 85.8 93.57 -7.77119 5.537 -1.403444 #> ds 5 parent 7 87.6 87.52 0.07909 5.208 0.015186 #> ds 5 parent 7 94.0 87.52 6.47909 5.208 1.244026 #> ds 5 parent 14 82.5 77.86 4.64101 4.687 0.990182 #> ds 5 parent 14 81.7 77.86 3.84101 4.687 0.819498 #> ds 5 parent 28 60.0 61.62 -1.61729 3.829 -0.422433 #> ds 5 parent 28 61.0 61.62 -0.61729 3.829 -0.161236 #> ds 5 parent 60 32.5 36.10 -3.59608 2.571 -1.398750 #> ds 5 parent 60 35.5 36.10 -0.59608 2.571 -0.231854 #> ds 5 parent 90 21.8 21.86 -0.06415 1.987 -0.032287 #> ds 5 parent 90 24.4 21.86 2.53585 1.987 1.276317 #> ds 5 parent 120 14.1 13.24 0.85643 1.724 0.496877 #> ds 5 parent 120 12.1 13.24 -1.14357 1.724 -0.663473